To solve this equation, we will first simplify it:

(x + 4 9/11) - 5 6/11 = 1 8/11

Convert 4 9/11 to an improper fraction:
4 9/11 = (4*11 + 9)/11 = 53/11

Convert 5 6/11 to an improper fraction:
5 6/11 = (5*11 + 6)/11 = 61/11

Now the equation becomes:
(x + 53/11) - 61/11 = 1 8/11

Combine the fractions:
x + 53/11 - 61/11 = 1 8/11
x - 8/11 = 1 8/11

Subtract 8/11 from both sides:
x = 1 8/11 + 8/11
x = 2

Therefore, the solution to the equation is x = 2.